3,581 research outputs found
Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps
Closed form expressions in terms of multi-sums of products have been given in
\cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de
Vries and potential Korteweg-de Vries maps obtained as so-called
-traveling wave reductions of the corresponding partial difference
equations. We prove the involutivity of these integrals with respect to
recently found symplectic structures for those maps. The proof is based on
explicit formulae for the Poisson brackets between multi-sums of products.Comment: 24 page
Isotope Spectroscopy
The measurement of isotopic ratios provides a privileged insight both into
nucleosynthesis and into the mechanisms operating in stellar envelopes, such as
gravitational settling. In this article, we give a few examples of how isotopic
ratios can be determined from high-resolution, high-quality stellar spectra. We
consider examples of the lightest elements, H and He, for which the isotopic
shifts are very large and easily measurable, and examples of heavier elements
for which the determination of isotopic ratios is more difficult. The presence
of 6Li in the stellar atmospheres causes a subtle extra depression in the red
wing of the 7Li 670.7 nm doublet which can only be detected in spectra of the
highest quality. But even with the best spectra, the derived Li abundance
can only be as good as the synthetic spectra used for their interpretation. It
is now known that 3D non-LTE modelling of the lithium spectral line profiles is
necessary to account properly for the intrinsic line asymmetry, which is
produced by convective flows in the atmospheres of cool stars, and can mimic
the presence of 6Li. We also discuss briefly the case of the carbon isotopic
ratio in metal-poor stars, and provide a new determination of the nickel
isotopic ratios in the solar atmosphere.Comment: AIP Thinkshop 10 "High resolution optical spectroscopy", invited
talk, AN in pres
The staircase method: integrals for periodic reductions of integrable lattice equations
We show, in full generality, that the staircase method provides integrals for
mappings, and correspondences, obtained as traveling wave reductions of
(systems of) integrable partial difference equations. We apply the staircase
method to a variety of equations, including the Korteweg-De Vries equation, the
five-point Bruschi-Calogero-Droghei equation, the QD-algorithm, and the
Boussinesq system. We show that, in all these cases, if the staircase method
provides r integrals for an n-dimensional mapping, with 2r<n, then one can
introduce q<= 2r variables, which reduce the dimension of the mapping from n to
q. These dimension-reducing variables are obtained as joint invariants of
k-symmetries of the mappings. Our results support the idea that often the
staircase method provides sufficiently many integrals for the periodic
reductions of integrable lattice equations to be completely integrable. We also
study reductions on other quad-graphs than the regular 2D lattice, and we prove
linear growth of the multi-valuedness of iterates of high-dimensional
correspondences obtained as reductions of the QD-algorithm.Comment: 40 pages, 23 Figure
PAH emission in the proplyd HST10: what is the mechanism behind photoevaporation?
Proplyds are photodissociation region (PDR)-like cometary cocoons around
young stars which are thought to originate through photo-evaporation of the
central protoplanetary disk by external UV radiation from the nearby OB stars.
This letter presents spatially resolved mid-infrared imaging and spectroscopy
of the proplyd HST10 obtained with the VLT/VISIR instrument. These observations
allow us to detect Polycyclic Aromatic Hydrocarbons (PAH) emission in the
proplyd photodissociation region and to study the general properties of PAHs in
proplyds for the first time. We find that PAHs in HST10 are mostly neutral and
at least 50 times less abundant than typical values found for the diffuse ISM
or the nearby Orion Bar. With such a low PAH abundance, photoelectric heating
is significantly reduced. If this low abundance pertains also to the original
disk material, gas heating rates could be too low to efficiently drive
photoevaporation unless other processes can be identified. Alternatively, the
model behind the formation of proplyds as evaporating disks may have to be
revised.Comment: 5 pages, 3 figures, 1 tabl
FUV and X-ray irradiated protoplanetary disks: a grid of models I. The disk structure
Context. Planets are thought to eventually form from the mostly gaseous (~99%
of the mass) disks around young stars. The density structure and chemical
composition of protoplanetary disks are affected by the incident radiation
field at optical, FUV, and X-ray wavelengths, as well as by the dust
properties.
Aims. The effect of FUV and X-rays on the disk structure and the gas chemical
composition are investigated. This work forms the basis of a second paper,
which discusses the impact on diagnostic lines of, e.g., C+, O, H2O, and Ne+
observed with facilities such as Spitzer and Herschel.
Methods. A grid of 240 models is computed in which the X-ray and FUV
luminosity, minimum grain size, dust size distribution, and surface density
distribution are varied in a systematic way. The hydrostatic structure and the
thermo-chemical structure are calculated using ProDiMo.
Results. The abundance structure of neutral oxygen is stable to changes in
the X-ray and FUV luminosity, and the emission lines will thus be useful
tracers of the disk mass and temperature. The C+ abundance distribution is
sensitive to both X-rays and FUV. The radial column density profile shows two
peaks, one at the inner rim and a second one at a radius r=5-10 AU. Ne+ and
other heavy elements have a very strong response to X-rays, and the column
density in the inner disk increases by two orders of magnitude from the lowest
(LX = 1e29 erg/s) to the highest considered X-ray flux (LX = 1e32 erg/s). FUV
confines the Ne+ ionized region to areas closer to the star at low X-ray
luminosities (LX = 1e29 erg/s). H2O abundances are enhanced by X-rays due to
higher temperatures in the inner disk and higher ionization fractions in the
outer disk. The line fluxes and profiles are affected by the effects on these
species, thus providing diagnostic value in the study of FUV and X-ray
irradiated disks around T Tauri stars. (abridged)Comment: 47 pages, accepted by Astronomy and Astrophysics, a high resolution
version of the paper is located at
http://www.astro.rug.nl/~meijerink/disk_paperI_xrays.pd
Modally Resolved Fabry-Perot Experiment with Semiconductor Waveguides
Based on the interaction between different spatial modes, semiconductor
Bragg-reflection waveguides provide a highly functional platform for non-linear
optics. Therefore, the control and engineering of the properties of each
spatial mode is essential. Despite the multimodeness of our waveguide, the
well-established Fabry-Perot technique for recording fringes in the optical
transmission spectrum can successfully be employed for a detailed linear
optical characterization when combined with Fourier analysis. A prerequisite
for the modal sensitivity is a finely resolved transmission spectrum that is
recorded over a broad frequency band. Our results highlight how the features of
different spatial modes, such as their loss characteristics and dispersion
properties, can be separated from each other allowing their comparison. The
mode-resolved measurements are important for optimizing the performance of such
multimode waveguides by tailoring the properties of their spatial modes.Comment: 8 pages, 7 figure
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